Page:Carroll - Euclid and His Modern Rivals.djvu/217

. § 6.] this is strangely inaccurate: the fourth condition is sufficient by itself to determine the line AI.

At p. 40 I notice the startling announcement that 'the simplest of all Polygons is the Triangle'! This is surely a new use for 'many'? I wonder if the writer is prepared to accept the statement that 'many people have swum across the Bosphorus' on the strength of Byron's

As a specimen of the wordy and unscientific style of the writer, take the following:—

'From any point O, one, and only one, perpendicular can be drawn to a given straight Line AB.



'Let O’ be the point on which O would fall if, the paper being folded along AB, the upper portion of the figure were turned down upon the lower portion. If from the points O, O’ straight Lines be drawn to any point whatever I on the line AB, the adjacent angles OIB, O’IB will be equal; for folding the paper again along AB and turning the upper portion down upon the lower, O falls on O’, I remains fixed, and the angle OIB exactly coincides with O’IB. Now in order that the Line OI may be perpendicular to AB, or, in other words, that OIB may be a right angle,